Advertisement

When has the sample mean as an estimator of a location or scale parameter high efficiency?

  • Lennart Bondesson
Article
  • 33 Downloads

Keywords

Stochastic Process Probability Theory Scale Parameter Mathematical Biology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. 1.
    Bondesson, L.: Characterizations of the gamma distribution. Teor. Veroyatnost. i Primenen. 18, 382–384 (1973)Google Scholar
  2. 2.
    Bondesson, L.: Characterizations of the normal and the gamma distributions. Z. Wahrscheinlichkeitstheorie und verw. Gebiete 26, 335–344 (1973)Google Scholar
  3. 3.
    Bondesson, L.: Characterizations of the gamma distribution and related laws. In Statistical Distributions in Scientific Work, Characterizations and Applications (Vol. III). G. P. Patil, S. Kotz, and J.K. Ord. Reidel: Dordrecht and Boston. 185–198 (1975)Google Scholar
  4. 4.
    Esseen, C.G.: Fourier analysis of distribution functions. Acta Math. 77, 1–124 (1945)Google Scholar
  5. 5.
    Kagan, A.M.: On the ɛ-admissibility of the sample mean as an estimator of location parameters. Sankhyā A 32, 37–40 (1970)Google Scholar
  6. 6.
    Kagan, A.M., Klebanov, L.B.: On the conditions of asymptotic ɛ-admissibility of the polynomial Pitman estimators of a location parameter and certain properties of information measures of closeness. In Statistical Distributions in Scientific Work, Characterizations and Applications (Vol. III). G. P. Patil, S. Kotz, and J. K. Ord. Reidel: Dordrecht and Boston. 173–184 (1975)Google Scholar
  7. 7.
    Kagan, A.M., Linnik, Yu.V., Rao, C.R.: Characterization Problems in Mathematical Statistics. New York: Wiley 1973Google Scholar
  8. 8.
    Kagan, A.M., Zinger, A.A.: Sample mean as an estimator of location parameter in presence of a nuisance scale parameter. Sankhyā A 35, 447–454 (1973)Google Scholar
  9. 9.
    Klebanov, L.B., Melamed, I.A.: On characterization of the normal and the gamma distributions by properties of Fisher information (in Russian). Zapiski Nauchnych Seminarov LOMI 43, 53–58 (1974)Google Scholar
  10. 10.
    Marcinkiewicz, J., Zygmund, A.: Sur les fonctions indépendant. Fund. Math. 29, 60–90 (1937)Google Scholar
  11. 11.
    Pitman, E.J.G.: The estimation of the location and scale parameters of a continuous population of any given form. Biometrika 30, 391–421 (1938)Google Scholar
  12. 12.
    Zinger, A.A.: A condition of ɛ-admissibility of the sample mean as an estimator of a location parameter in presence of a nuisance scale parameter (in Russian). Zapiski Nauchnych Seminarov LOMI 61, 25–37 (1976)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Lennart Bondesson
    • 1
    • 2
  1. 1.National Central Bureau of StatisticsStockholm 27Sweden
  2. 2.Department of Mathematical StatisticsUniversity of LundLundSweden

Personalised recommendations